Problem: Which of the following numbers is a multiple of 9? ${42,43,84,90,103}$
Explanation: The multiples of $9$ are $9$ $18$ $27$ $36$ ..... In general, any number that leaves no remainder when divided by $9$ is considered a multiple of $9$ We can start by dividing each of our answer choices by $9$ $42 \div 9 = 4\text{ R }6$ $43 \div 9 = 4\text{ R }7$ $84 \div 9 = 9\text{ R }3$ $90 \div 9 = 10$ $103 \div 9 = 11\text{ R }4$ The only answer choice that leaves no remainder after the division is $90$ $ 10$ $9$ $90$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $90$ $90 = 2\times3\times3\times5 9 = 3\times3$ Therefore the only multiple of $9$ out of our choices is $90$. We can say that $90$ is divisible by $9$.